You will lose access to theme/plugin downloads, updates and support when your license expires. Your website will not stop working but your theme or plugin will eventually become outdated which can cause problems.
You should renew your license to continue receiving updates, which address compatibility with new versions of WordPress and browsers, contain bug fixes and often include enhancements and new features. Renewal also provides you with an additional year of one on one support. As software, it is recommended to always run the latest version of WordPress, themes and plugins for stability and security – if for no other reason.